In my opinion, Although Deidara seems more dangerous than Sasori, I still believe Sasori can take him.
Why?
Well, first let's look at their personalities.
While Deidara is just playing immature, because that's what he always did, Sasori is calculated.
First example:
While Deidara seemed to want to grab Naruto as well, not thinking what are the dangers that could happen, Sasori was more calculated and didn't let himself rushed and as well respected the rules
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So, while Deidara is a hot-headed and only talkes about art all the time not calculating too much his moves, letting holes throughout the fight, Sasori is calculated and every move he takes is well thought.
2. Even Deidara recognized Sasori as his boss, and we see in this panel that Sasori doesn't hold himself in attacking him. Although this we could consider it a warning, more than an attack.
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Now let's look at Sasori's abilities.
What I grant you from the beginning is that on a larger scale, Deidara's attacks could seem even more dangerous. But what makes Sasori far superior than him is the way he uses his techniques.
Plus battle experiences! As we can see here, even Sakura realises that the difference in battle experiences between her and them is HUGE.
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Now let's take a look at Hiruko, Sasori's primary puppet:
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What do we know Hiruko has?
Well:
A puppet that serves as armor and as weapon in the same time:
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All weapons that he possesed on Hiruko were coated in poison and you cannot expect them from where they come, as Chyio herslef states here that you need to know a puppeteer in order to be able to deflect his attacks/win against him.
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So if you look at it, Deidara can be taken down by a simple surprise attack.
We fairly know that Deidara takes a bit of time before preparing that Dragon and any weapon he has in his arsenal.
So in order to be able to fly on that dragon, or whatever he creates, before that he has to mold the clay. Until then, he can be poisoned by Sasori as we know that Sasori hates to wait.
And he has 3 means.
Senbon (needles filled with poison) - and those are really fast as we've seen.
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The left arm that launches the same poisonous senbon in all directions:
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Not to mention that Hiruko seemed like made from materials very durable and only Sakura's punch was able to break it because of her "super-human strenght inherited from Tsunade" as Chyio stated.
So, Deidara from the start would have to worry about 2 things: wheter to make his dragon to be able to fly quicker from Sasori's range or to those small clay animals to be able to counteract Sasori's attacks but it would still let him open to Sasori's poison needles and it's not like Sasori won't move with Hiruko from Deidara's range of attack.
You'll say that he didn't moved back then.
Well, he didn't because he was expecting that Hiruko's arsenal would suffice against Sakura and Chyio, what it didn't.
And as it was stated, only a puppeteer can see through other's puppeteer attack:
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And not to mention that those secrets were taught by Chiyo herself. So that's why she was able to see through them.
I doubt Sasori would let Deidara know his secrets.
Now, let's presume the second scenario.
Deidara has his little flying things.
Now, Sasori can take out his heavy artilery.
The third Kazekage:
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We have seen that the third Kazekage can move really fast.
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This would be another minus for Deidara's time-taking clay making. Because he could be poisoned and cut in the next seconds:
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We know that here if it wouldn't have been for Chyio, Sakura would've been done.
That is, if he stays on the bird and doesn't hide himself inside the mouth of his creatures, like here:
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Now if he's inside... Remember this:
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He could utilise this in order to shred the clay and find Deidara and take him out.
How? Well... Deidara has to breath, doesn't he? We all know what the third Kazekage has in it's arsenal.
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Now, we can safely assume that the only thing that remains for Deidara, is use an explosion as Sakura did herself (used an explosion tag to get out of the poisoned gas)
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But then again, Sasori could draw the Kazekage out of the attack range and then, use the poisoned Kunai:
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I bet that through the explosion he wouldn't expect that.
Now assuming it survives this as well, Deidara has to pass on the heavy artilery, like C 123457887, you name it.
Third Kazekage's Kekke Genkai was the Iron Sand.
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What do we know about the Iron Sand? Well, as Chiyo stated by herself:
It allows you to make iron sand into
any shape or form. And of course that it provides you with means to make a weapon for any situation.
Now taking into consideration magnetism... and his Iron Sand, I wonder why into Sasori's mind never passed the idea to use the sandaime's sand as a floating piece of sand providing him to be as well for large range for a period of time, like Gaara did with his sand?
Because if this is possible, and I believe it fairly is, then Deidara would be long gone, to be honest.
And now, we have these:
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I wonder how would Deidara make those dissapear? He has no way. An explosion won't do any damage to the iron. The only possibility to melt the iron is if you boil it at 1000 degrees.
Now we know that at some point, they were able to defeat Sasori because Sakura was there, and basically, she developed a plan to lure Sasori in using the puppet as close to her in order to break it, because if not, she was sure that it was over because the weapons that he posessed throughout the Third Kazekage, would've been lethal for both of them.
I mean, look at this:
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And it's all filled with poison. I don't see Deidara surviving this, sorry.
Even if he goes C4, Sasori is able to build around himself and the puppet some sort of cube in order to avoid Deidara's biggest blow.
So my pledge is finished here. No need to take out the 100 puppets.
Anyway, really nice thread!

As always.